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Differentiation of eigen(::Symmetric) #575

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Merged
KristofferC merged 6 commits into from
May 13, 2022
Merged

Differentiation of eigen(::Symmetric) #575

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e11a6a7
Make eigen(::Symmetric) work
KnutAM Feb 13, 2022
becc260
Add tests for eigen
KnutAM Feb 13, 2022
750f1fe
Add support for autodiff of static symmetric tensors
KnutAM May 9, 2022
1e8eaaf
Add tests for sym static eigen diff
KnutAM May 9, 2022
85c79a0
Fix typo in test
KnutAM May 9, 2022
40e25a2
Use Calculus.jl for test eigendiff
KnutAM May 12, 2022
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15 changes: 14 additions & 1 deletion src/dual.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -658,6 +658,12 @@ function LinearAlgebra.eigvals(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N
Dual{Tg}.(λ, tuple.(parts...))
end

function LinearAlgebra.eigvals(A::Symmetric{<:Dual{Tg,T,N}, <:StaticArrays.StaticMatrix}) where {Tg,T<:Real,N}
λ,Q = eigen(Symmetric(value.(parent(A))))
parts = ntuple(j -> diag(Q' * getindex.(partials.(A), j) * Q), N)
Dual{Tg}.(λ, tuple.(parts...))
end

function LinearAlgebra.eigvals(A::Hermitian{<:Complex{<:Dual{Tg,T,N}}}) where {Tg,T<:Real,N}
λ,Q = eigen(Hermitian(value.(real.(parent(A))) .+ im .* value.(imag.(parent(A)))))
parts = ntuple(j -> diag(real.(Q' * (getindex.(partials.(real.(A)) .+ im .* partials.(imag.(A)), j)) * Q)), N)
Expand All @@ -682,7 +688,14 @@ end

function LinearAlgebra.eigen(A::Symmetric{<:Dual{Tg,T,N}}) where {Tg,T<:Real,N}
λ = eigvals(A)
_,Q = eigen(SymTridiagonal(value.(parent(A).dv),value.(parent(A).ev)))
_,Q = eigen(Symmetric(value.(parent(A))))
parts = ntuple(j -> Q*_lyap_div!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N)
Eigen(λ,Dual{Tg}.(Q, tuple.(parts...)))
end

function LinearAlgebra.eigen(A::Symmetric{<:Dual{Tg,T,N}, <:StaticArrays.StaticMatrix}) where {Tg,T<:Real,N}
λ = eigvals(A)
_,Q = eigen(Symmetric(value.(parent(A))))
parts = ntuple(j -> Q*_lyap_div!(Q' * getindex.(partials.(A), j) * Q - Diagonal(getindex.(partials.(λ), j)), value.(λ)), N)
Eigen(λ,Dual{Tg}.(Q, tuple.(parts...)))
end
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8 changes: 8 additions & 0 deletions test/JacobianTest.jl
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Expand Up @@ -235,6 +235,14 @@ end
@testset "eigen" begin
@test ForwardDiff.jacobian(x -> eigvals(SymTridiagonal(x, x[1:end-1])), [1.,2.]) ≈ [(1 - 3/sqrt(5))/2 (1 - 1/sqrt(5))/2 ; (1 + 3/sqrt(5))/2 (1 + 1/sqrt(5))/2]
@test ForwardDiff.jacobian(x -> eigvals(Symmetric(x*x')), [1.,2.]) ≈ [0 0; 2 4]

x0 = [1.0, 2.0];
ev1(x) = eigen(Symmetric(x*x')).vectors[:,1]
@test ForwardDiff.jacobian(ev1, x0) ≈ Calculus.finite_difference_jacobian(ev1, x0)
ev2(x) = eigen(SymTridiagonal(x, x[1:end-1])).vectors[:,1]
@test ForwardDiff.jacobian(ev2, x0) ≈ Calculus.finite_difference_jacobian(ev2, x0)
x0_static = SVector{2}(x0)
@test ForwardDiff.jacobian(ev1, x0_static) ≈ Calculus.finite_difference_jacobian(ev1, x0)
end

@testset "type stability" begin
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